Abstract A rigorous non-existence proof for runaway solutions in the finite-size model of the electron is given. Since a consistent point limit, such as the Lorentz-Dirac equation claims to be, should not exhibit features which are completely missing in the more general theory of finite extension, it is proposed that the point-like approximation of the finite-size theory be the integrodifferential formulation of the Lorentz-Dirac theory. This point of view is supported by a new discussion of the hyperbolic motion in the latter theory.
The equation of motion of a high speed test particle in the field of a spherical mass is discussed for a parametric range of gravitational theories, including general relativity. It is shown how in principle such hyperbolic orbits may discriminate between these theories.
Electric field of a point charge in truncated hyperbolic motion
